基于POT模型的我国地震损失分布研究  

Study of earthquake losses distribution in China based on POT model

作　　者：许一涵 尤添革[1,2] 温芫姚 宁静 肖扬岚[1,2] 尤学敏 XU Yihan;YOU Tiange;WEN Yuanyao;NING Jing;XIAO Yanglan;YOU Xuemin(College of Computer and Information Sciences,Fujian Agriculture and Forestry University,Fuzhou 350002,China;Statistical Information Research Center of Fujian Province,Fuzhou 350002,China;State Grid Communication Yili Technology Co.Ltd.,Fuzhou 350002,China)

机构地区：[1]福建农林大学计算机与信息学院,福州350002 [2]福建省统计信息研究中心,福州350002 [3]国网信通亿力科技有限责任公司,福州350002

出　　处：《哈尔滨商业大学学报（自然科学版）》2023年第4期446-452,共7页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：福建省社会科学规划项目(FJ2018B063)。

摘　　要：确定地震灾害损失分布有利于防灾减灾及灾后赔偿工作的开展.运用超越阈值模型(POT)、马尔科夫链蒙特卡洛估计(MCMC)等研究方法,探索我国地震损失分布特征,并进行参数估计.POT模型能够有效运用极端数据.研究结果显示,我国地震损失具有“尖峰、厚尾”的特征,适合使用广义Pareto分布(GPD)拟合,且通过分布拟合图、残差QQ图等检验.经Hill图、均值超额函数图比较不同阈值下GPD分布的参数估计,得到阈值μ=3.4较合适并建立模型,使用极大似然法进行参数估计且通过检验.考虑到小样本情形下极大似然法可能失效的问题,使用蒙特卡洛法估计参数,并比较不同样本量下极大似然法和蒙特卡洛法的参数估计结果,得到小样本情形下蒙特卡洛法估计效果更理想.Determining the distribution of earthquake damage losses is conducive to disaster prevention and mitigation and post-disaster compensation.In this paper,the Beyond Threshold Model(POT)and the Markov Chain Monte Carlo Estimation(MCMC)were used to explore the distribution characteristics of earthquake loss in China and estimate the parameters.POT models can effectively use extreme data.The results showed that China s seismic loss had the characteristics of“spike and thick tail”,which was suitable for generalized Pareto distribution(GPD)fitting,and passed the distribution fitting plot,residual QQ plot and other tests.The parameter estimation of GPD distribution under different thresholds was compared by Hill plot and mean excess function plot,and the thresholdμ=3.4 was more suitable and the model was established,and the parameter estimation was carried out by the maximum likelihood method and passed the test.Considering the problem that the maximum likelihood method may fail in the small sample case,the MCMC method was used to estimate the parameters,and the parameter estimation results of the maximum likelihood method and MCMC method were compared under different data amounts,and the MCMC method was obtained to be more satisfactory in the small sample case.

关 键 词：地震灾害 GPD分布 厚尾特征 MCMC法 极大似然估计 

分 类 号：O212.8[理学—概率论与数理统计]